Please do all calculations using only hand calculator. This will help you understand the basic proportionality rule for getting expected values.1. The discussion of the polio data implies that a statsig X2 is not adequate evidence that the vaccine was effective. Why not? What general principle does this illustrate?2. In the polio experiment:

a.

Why should a preliminary power calculation be made?

b.

What criticism might be made of the N in this experiment?

c.

By analogy to Section 4.3 on power for Anova, guess what item of information is needed for a power calculation for chi-square.

3. In one of the final tests of Clever Hans, the mathematical horse of Chapter 8, Hans was instructed to perform a simple arithmetic task, such as adding two numbers. On each trial, Mr. von Osten would whisper one of the numbers in Hans' ear, following which Professor Pfungst would whisper the other number. On some of these trials, one or both men knew the answer; on these trials, Hans got 29 right and 2 wrong. On other trials, neither man knew the answer; on these trials, Hans got 3 right and 28 wrong (Pfungst, 1965, p. 37.)

a.

What is the null hypothesis in this 2 × 2 contingency table?

b.

Is chi-square really applicable with these small frequencies of 2 and 3?

c.

Show that X2 = 43.66.

d.

Show that the 95% confidenceinterval is.84 ±.14.

e.

Is this chi-square test really needed?

4. In the field study of smoking prevention in the Appendix to Chapter 3, 19%, 24%, and 27% of the cases in the three treatment conditions had not smoked at the three-month mark. Assume each group had exactly 1000 subjects. Show that X2 = 18.26.

5. A clinical trial (= experiment) extending over several years showed that breast cancer was developed by 216 of 6707 women on placebo control, and by 115 of 6681 women on the drug tamoxifen. Should the Food and Drug Administration approve tamoxifen for prescription by doctors?

6. In a field experiment in a nursing home, one group of residents received a treatment that emphasized their responsibility to make their own choices and control their own lives. A comparison group received a treatment that emphasized the responsibility of the staff to care for them and make them happy

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